((13)/6) Option 1: 1/2 Option 2: 1/√2 Option 3: 1/√3 Option 4: √3

Answer: 1/2. Solution: (13)/6 = (12)/6 + ()/6 = 2 + ()/6 (In degrees: 390^ = 360^ + 30^) Sine repeats after every 2 (one full round), so adding 2 does not change its value: ((13)/6) = (()/6) = 30^ = 1/2 Therefore, ((13)/6) = 1/2.

Geometry

Trigonometry

Conceptual

$\sin(\frac{13\pi}{6})$

$\frac{1}{2}$

$\frac{1}{\sqrt{2}}$

$\frac{1}{\sqrt{3}}$

$\sqrt{3}$

✅ Correct Option: 1

$\dfrac{13\pi}{6} = \dfrac{12\pi}{6} + \dfrac{\pi}{6}$

$= 2\pi + \dfrac{\pi}{6}$

(In degrees: $390^\circ = 360^\circ + 30^\circ$ )

Sine repeats after every $2\pi$ (one full round), so adding $2\pi$ does not change its value:

$\sin\left(\dfrac{13\pi}{6}\right) = \sin\left(\dfrac{\pi}{6}\right)$

$= \sin 30^\circ$

$= \dfrac{1}{2}$

Therefore, $\sin\left(\dfrac{13\pi}{6}\right) = \dfrac{1}{2}$ .

sin⁡(13π6)\sin(\frac{13\pi}{6})sin(613π​)

Solution

Keyboard Shortcuts

IPMAT Rohtak Past Year Questions (Topic-Wise)

$\sin(\frac{13\pi}{6})$